Question

slove the equation. 5=55(1.3)^x. for x using logs.

Answer 1

start with
\[\frac{1}{11}=(1.3)^x\] then use the change of base formula in one step to get
\[x=\frac{\ln(\frac{1}{11})}{\ln(1.3)}\]

Answer 2

why its 1/11? where is it come from.

Answer 3

you need it to look like \(A=b^x\) so you have to divide by 55 as a first step

Answer 4

once you have \(A=b^x\) you can go right to \(x=\frac{\ln(A)}{\ln(b)}\) but you have to get rid of the coefficient first

Answer 5

OK, I got it. but what is change of base formula? and how do you calculate X=In(1/11)/In(1.3)?

Answer 6

a calculator is the only way to solve this if you want a decimal

Answer 7

I have a calculator with me. but theres no "In "botten

Answer 8

ok that was wrong

Answer 9

change of base says
\[\log_a(x)=\frac{\log_b(x)}{\log_b(a)}\]

Answer 10

but in real life you need to use \(\ln(x)\) or \(\log_{10}(x)\) because that is all you have on your calculator

Answer 11

there are a multitude of on line calculators, i like this one
http://www.wolframalpha.com/input/?i=ln%281%2F11%29%2Fln%281.3%29

Answer 12

Thank you so much for helping me with this. I am so stuck with math but i want to do well in the end.

Answer 13

don't forget, if you want to solve
\[b^x=A\] for \(x\) go right to \[x=\frac{\ln(A)}{\ln(b)}\]

yw